897 research outputs found
Forward refutation for Gödel-Dummett Logics
We propose a refutation calculus to check the unprovability of a formula in Gödel-Dummett logics. From refutations we can directly extract countermodels for unprovable formulas, moreover the calculus is designed so to support a forward proof-search strategy that can be understood as a top-down construction of a model
Completeness of a first-order temporal logic with time-gaps
The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov
A repetition-free hypersequent calculus for first-order rational Pavelka logic
We present a hypersequent calculus \text{G}^3\text{\L}\forall for
first-order infinite-valued {\L}ukasiewicz logic and for an extension of it,
first-order rational Pavelka logic; the calculus is intended for bottom-up
proof search. In \text{G}^3\text{\L}\forall, there are no structural rules,
all the rules are invertible, and designations of multisets of formulas are not
repeated in any premise of the rules. The calculus \text{G}^3\text{\L}\forall
proves any sentence that is provable in at least one of the previously known
hypersequent calculi for the given logics. We study proof-theoretic properties
of \text{G}^3\text{\L}\forall and thereby provide foundations for proof
search algorithms.Comment: 21 pages; corrected a misprint, added an appendix containing errata
to a cited articl
Resource Bounded Unprovability of Computational Lower Bounds
This paper introduces new notions of asymptotic proofs,
PT(polynomial-time)-extensions, PTM(polynomial-time Turing
machine)-omega-consistency, etc. on formal theories of arithmetic including PA
(Peano Arithmetic). This paper shows that P not= NP (more generally, any
super-polynomial-time lower bound in PSPACE) is unprovable in a
PTM-omega-consistent theory T, where T is a consistent PT-extension of PA. This
result gives a unified view to the existing two major negative results on
proving P not= NP, Natural Proofs and relativizable proofs, through the two
manners of characterization of PTM-omega-consistency. We also show that the
PTM-omega-consistency of T cannot be proven in any PTM-omega-consistent theory
S, where S is a consistent PT-extension of T.Comment: 78 page
Paradoxes of rational agency and formal systems that verify their own soundness
We consider extensions of Peano arithmetic which include an assertibility
predicate. Any such system which is arithmetically sound effectively verifies
its own soundness. This leads to the resolution of a range of paradoxes
involving rational agents who are licensed to act under precisely defined
conditions.Comment: 10 page
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